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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1225.1.g.a \(2\) \(0.611\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{4}+iq^{9}+q^{11}-q^{16}-iq^{29}+\cdots\)
1225.1.g.b \(4\) \(0.611\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}+\beta _{2}q^{9}+\cdots\)
1225.1.i.a \(2\) \(0.611\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)
1225.1.i.b \(2\) \(0.611\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)
1225.1.j.a \(4\) \(0.611\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{2}q^{9}+\cdots\)
1225.1.q.a \(4\) \(0.611\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{4}-\zeta_{12}^{5}q^{9}+\zeta_{12}^{4}q^{11}+\cdots\)
1225.1.q.b \(8\) \(0.611\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
1225.2.a.a \(1\) \(9.782\) \(\Q\) None None \(-2\) \(1\) \(0\) \(0\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{9}+\cdots\)
1225.2.a.b \(1\) \(9.782\) \(\Q\) None None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}-2q^{9}+\cdots\)
1225.2.a.c \(1\) \(9.782\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(-\) \(q-q^{2}-q^{4}+3q^{8}-3q^{9}+4q^{11}+\cdots\)
1225.2.a.d \(1\) \(9.782\) \(\Q\) None None \(-1\) \(1\) \(0\) \(0\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}-2q^{9}+\cdots\)
1225.2.a.e \(1\) \(9.782\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(-\) \(q+q^{3}-2q^{4}-2q^{9}-3q^{11}-2q^{12}+\cdots\)
1225.2.a.f \(1\) \(9.782\) \(\Q\) None None \(1\) \(-1\) \(0\) \(0\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}-2q^{9}+\cdots\)
1225.2.a.g \(1\) \(9.782\) \(\Q\) None None \(1\) \(1\) \(0\) \(0\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}-2q^{9}+\cdots\)
1225.2.a.h \(1\) \(9.782\) \(\Q\) None None \(2\) \(-3\) \(0\) \(0\) \(-\) \(q+2q^{2}-3q^{3}+2q^{4}-6q^{6}+6q^{9}+\cdots\)
1225.2.a.i \(1\) \(9.782\) \(\Q\) None None \(2\) \(-1\) \(0\) \(0\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-2q^{9}+\cdots\)
1225.2.a.j \(1\) \(9.782\) \(\Q\) None None \(2\) \(3\) \(0\) \(0\) \(-\) \(q+2q^{2}+3q^{3}+2q^{4}+6q^{6}+6q^{9}+\cdots\)
1225.2.a.k \(2\) \(9.782\) \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(q+(-1+\beta )q^{2}+(-1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
1225.2.a.l \(2\) \(9.782\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(0\) \(-\) \(q-q^{2}+2\beta q^{3}-q^{4}-2\beta q^{6}+3q^{8}+\cdots\)
1225.2.a.m \(2\) \(9.782\) \(\Q(\sqrt{2}) \) None None \(-2\) \(2\) \(0\) \(0\) \(-\) \(q+(-1+\beta )q^{2}+(1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
1225.2.a.n \(2\) \(9.782\) \(\Q(\sqrt{5}) \) None None \(-1\) \(-2\) \(0\) \(0\) \(+\) \(q-\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
1225.2.a.o \(2\) \(9.782\) \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(q-\beta q^{2}+(3+\beta )q^{4}+(-5-2\beta )q^{8}+\cdots\)
1225.2.a.p \(2\) \(9.782\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{3}+(2-\beta )q^{6}-2\beta q^{8}+\cdots\)
1225.2.a.q \(2\) \(9.782\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-\beta q^{3}-2q^{4}+2q^{9}-3q^{11}+2\beta q^{12}+\cdots\)
1225.2.a.r \(2\) \(9.782\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) \(+\) \(q+\beta q^{2}+(1-\beta )q^{3}+(-2+\beta )q^{6}-2\beta q^{8}+\cdots\)
1225.2.a.s \(2\) \(9.782\) \(\Q(\sqrt{17}) \) None None \(1\) \(-1\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+4q^{6}+\cdots\)
1225.2.a.t \(2\) \(9.782\) \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+(3+\beta )q^{4}+(5+2\beta )q^{8}-3q^{9}+\cdots\)
1225.2.a.u \(2\) \(9.782\) \(\Q(\sqrt{5}) \) None None \(1\) \(2\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+(2-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
1225.2.a.v \(2\) \(9.782\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(0\) \(-\) \(q+q^{2}-2\beta q^{3}-q^{4}-2\beta q^{6}-3q^{8}+\cdots\)
1225.2.a.w \(3\) \(9.782\) 3.3.257.1 None None \(-1\) \(-3\) \(0\) \(0\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1225.2.a.x \(3\) \(9.782\) 3.3.257.1 None None \(-1\) \(3\) \(0\) \(0\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1225.2.a.y \(3\) \(9.782\) 3.3.257.1 None None \(1\) \(-3\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1225.2.a.z \(3\) \(9.782\) 3.3.257.1 None None \(1\) \(3\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1225.2.a.ba \(4\) \(9.782\) \(\Q(\sqrt{2}, \sqrt{5})\) None None \(-6\) \(0\) \(0\) \(0\) \(+\) \(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+3\beta _{2}q^{4}+\cdots\)
1225.2.a.bb \(4\) \(9.782\) \(\Q(\zeta_{24})^+\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+4q^{4}+3\beta _{2}q^{6}+\cdots\)
1225.2.a.bc \(4\) \(9.782\) \(\Q(\sqrt{2}, \sqrt{5})\) None None \(6\) \(0\) \(0\) \(0\) \(-\) \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+3\beta _{2}q^{4}+(2\beta _{1}+\cdots)q^{6}+\cdots\)
1225.2.b.a \(2\) \(9.782\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+3iq^{3}-2q^{4}-6q^{6}-6q^{9}+\cdots\)
1225.2.b.b \(2\) \(9.782\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-2q^{4}+6q^{6}-6q^{9}+\cdots\)
1225.2.b.c \(2\) \(9.782\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+3iq^{8}+3q^{9}+4q^{11}+\cdots\)
1225.2.b.d \(2\) \(9.782\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2q^{4}+2q^{9}-3q^{11}-2iq^{12}+\cdots\)
1225.2.b.e \(4\) \(9.782\) \(\Q(i, \sqrt{21})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-4+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3})q^{8}+\cdots\)
1225.2.b.f \(4\) \(9.782\) \(\Q(i, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
1225.2.b.g \(4\) \(9.782\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
1225.2.b.h \(4\) \(9.782\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
1225.2.b.i \(4\) \(9.782\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-2-\zeta_{8}^{3})q^{6}+\cdots\)
1225.2.b.j \(4\) \(9.782\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(2+\zeta_{8}^{3})q^{6}+\cdots\)
1225.2.b.k \(4\) \(9.782\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(2\beta _{1}+2\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1225.2.b.l \(6\) \(9.782\) 6.0.4227136.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
1225.2.b.m \(6\) \(9.782\) 6.0.4227136.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{3}-\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
1225.2.b.n \(8\) \(9.782\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{3})q^{2}+(-\beta _{5}+\beta _{7})q^{3}+\cdots\)
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